密频近线性系统的主共振与响应饱和现象

为了探讨在系统作强迫振动的过程中非线性耦合对于密集模态相互作用的影响,在本文中考察了具有密集的线性自然频率的近线性(弱非线性)系统的主共振,通过与非线性耦合能有关的平均Lagrange函数表示非线性耦合力对模态运动的影响,提出了一种列出模态运动的调幅调相方程(调制方程)的简便方法,并在此基础上讨论了密频近线性系统出现响应饱和现象的可能性,举例说明求饱和解的步骤,论述饱和解的存在与稳定性条件,从而表明密频内共振是继2:1内共振之后又一可能实现响应饱和的途径。

On the Main Resonance and Response Saturation in an Almost Linear System with Closely Spaced Natural Frequencies

In order to investigate the interaction between the main (external) resonance and the IRCF (internal resonance due to closely spaced natural frequencies). we present a method to facilitate the formulation of equations for amplitude-and-phase-modulated response.and discuss the possibility of the occurrence of response saturation. This paper ends with a simple example of a system with cubic non-linearity to study the existence and stability of the steady state response under the conditions of main resonance and IRCF.